Strong subdifferentiability and local Bishop–Phelps–Bollobás properties

Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.Fil: Dantas, Sheldon. Czech Technical University in Prague; República ChecaFil: Kim, Sun Kwang. Chungbuk National University; Corea del SurFil: Lee, Han Ju. Dongguk University, Seoul; Corea del SurFil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; Argentina. Comisión Nacional de Energía Atómica. Fundación José A. Balseiro; Argentin

Quantum electromagnetic field in a three dimensional oscillating cavity

We compute the photon creation inside a perfectly conducting, three dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and (generalized) Neumann type, we analyze as a preliminary step the dynamical Casimir effect for a scalar field satisfying generalized Neumann boundary conditions. We show that particle production is enhanced with respect to the case of Dirichlet boundary conditions. Then we consider the transverse electric and transverse magnetic polarizations of the electromagnetic field. For resonant frequencies, the total number of photons grows exponentially in time for both polarizations, the rate being greater for transverse magnetic modes.Comment: 11 pages, 1 figur

Resonant photon creation in a three dimensional oscillating cavity

We analyze the problem of photon creation inside a perfectly conducting, rectangular, three dimensional cavity with one oscillating wall. For some particular values of the frequency of the oscillations the system is resonant. We solve the field equation using multiple scale analysis and show that the total number of photons inside the cavity grows exponentially in time. This is also the case for slightly off-resonance situations. Although the spectrum of a cavity is in general non equidistant, we show that the modes of the electromagnetic field can be coupled, and that the rate of photon creation strongly depends on this coupling. We also analyze the thermal enhancement of the photon creation.Comment: 13 pages. New section on off-resonance motion is included. To appear in Physical Review

Solutions of the Schroedinger equation for piecewise harmonic potentials: Remarks on the asymptotic behavior of the wave functions

We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for |x|>a and by an arbitrary function for |x|<a, using elementary methods. The study of this problem sheds light on usual errors made in discussions of the asymptotic behavior of the eigenfunctions of the quantum harmonic oscillator and can also be used for the analysis of the eigenfunctions of the hydrogen atom. We present explicit results for the energy levels of a potential of this class, used to model the confinement of electrons in nanostructures.Fil: Mazzitelli, Francisco Diego. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mazzitelli, Martin Diego. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Soubelet, Pedro Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

On the polynomial lindenstrauss theorem

Under certain hypotheses on the Banach space X, we show that the set of N-homogeneous polynomials from X to any dual space, whose Aron-Berner extensions are norm attaining, is dense in the space of all continuous N-homogeneous polynomials. To this end we prove an integral formula for the duality between tensor products and polynomials. We also exhibit examples of Lorentz sequence spaces for which there is no polynomial Bishop-Phelps theorem, but our results apply. Finally we address quantitative versions, in the sense of Bollobás, of these results.Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

Multilinear Marcinkiewicz-Zygmund inequalities

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on (Formula presented.)-valued extensions of linear operators. We show that for certain (Formula presented.), there is a constant (Formula presented.) such that for every bounded multilinear operator (Formula presented.) and functions (Formula presented.), the following inequality holds (Formula presented.)In some cases we also calculate the best constant (Formula presented.) satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators.Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Mazzitelli, Martin Diego. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional del Comahue. Centro Reg.universidad Bariloche. Departamento de Matemática; ArgentinaFil: Ombrosi, Sheldy Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentin

Local Bishop–Phelps–Bollobás properties

In this paper we introduce some local versions of Bishop–Phelps–Bollobás type property for operators. That is, the function η which appears in their definitions depends not only on a given ε > 0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investigate those properties and show differences between local and uniform versions.Fil: Dantas, Sheldon. Pohang University Of Science And Technology; Corea del SurFil: Kim, Sun Kwang. Chungbuk National University; Corea del SurFil: Lee, Han Ju. Dongguk University; Corea del SurFil: Mazzitelli, Martin Diego. Universidad Nacional del Comahue. Facultad de Economía y Administración; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Omicron Breakthrough Infection after Heterologous Prime-Boost Vaccination Induces a Vigorous Antibody Response

Infection with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant is usually asymptomatic or mild and appears to be poorly immunogenic at least in unvaccinated individuals. Here, we found that health care workers vaccinated with 2 doses of Sputnik V and a booster dose of ChAdOx1 mount a vigorous neutralizing-Antibody response after Omicron breakthrough infection.Fil: Varese, Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Mazzitelli, Bianca. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Erra Diaz, Fernando Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Kjolhede, María Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Ojeda, Diego Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Vellicce, Alejandra Fabiana. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Arto, Penélope. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Cicero, Carla. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Pascowsky, María. Hospital Nacional Profesor Alejandro Posadas; ArgentinaFil: Figueras, Laura Victoria. Hospital Central de San Isidro; ArgentinaFil: Broese, Bárbara. Hospital Central de San Isidro; ArgentinaFil: Dávila, Rosa. Gobierno de la Provincia de San Luis. Hospital Policlinico Regional Juan Domingo Peron.; ArgentinaFil: Zarlenga, Rocío. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Rivelli, Federico Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Verruno, Camila. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Silenzi, Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Beltran, Ivana Romina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Gamarnik, Andrea Vanesa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Ceballos, Ana. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; ArgentinaFil: Zala, Carlos. Hospital Central de San Isidro; ArgentinaFil: Badolati, Adelina. Hospital Nacional Profesor Alejandro Posadas; ArgentinaFil: Geffner, Jorge Raúl. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas en Retrovirus y Sida. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Biomédicas en Retrovirus y Sida; Argentin

Clinical phenotypes and outcomes in children with multisystem inflammatory syndrome across SARS-CoV-2 variant eras: a multinational study from the 4CE consortiumResearch in context

Summary: Background: Multisystem inflammatory syndrome in children (MIS-C) is a severe complication of SARS-CoV-2 infection. It remains unclear how MIS-C phenotypes vary across SARS-CoV-2 variants. We aimed to investigate clinical characteristics and outcomes of MIS-C across SARS-CoV-2 eras. Methods: We performed a multicentre observational retrospective study including seven paediatric hospitals in four countries (France, Spain, U.K., and U.S.). All consecutive confirmed patients with MIS-C hospitalised between February 1st, 2020, and May 31st, 2022, were included. Electronic Health Records (EHR) data were used to calculate pooled risk differences (RD) and effect sizes (ES) at site level, using Alpha as reference. Meta-analysis was used to pool data across sites. Findings: Of 598 patients with MIS-C (61% male, 39% female; mean age 9.7 years [SD 4.5]), 383 (64%) were admitted in the Alpha era, 111 (19%) in the Delta era, and 104 (17%) in the Omicron era. Compared with patients admitted in the Alpha era, those admitted in the Delta era were younger (ES −1.18 years [95% CI −2.05, −0.32]), had fewer respiratory symptoms (RD −0.15 [95% CI −0.33, −0.04]), less frequent non-cardiogenic shock or systemic inflammatory response syndrome (SIRS) (RD −0.35 [95% CI −0.64, −0.07]), lower lymphocyte count (ES −0.16 × 109/uL [95% CI −0.30, −0.01]), lower C-reactive protein (ES −28.5 mg/L [95% CI −46.3, −10.7]), and lower troponin (ES −0.14 ng/mL [95% CI −0.26, −0.03]). Patients admitted in the Omicron versus Alpha eras were younger (ES −1.6 years [95% CI −2.5, −0.8]), had less frequent SIRS (RD −0.18 [95% CI −0.30, −0.05]), lower lymphocyte count (ES −0.39 × 109/uL [95% CI −0.52, −0.25]), lower troponin (ES −0.16 ng/mL [95% CI −0.30, −0.01]) and less frequently received anticoagulation therapy (RD −0.19 [95% CI −0.37, −0.04]). Length of hospitalization was shorter in the Delta versus Alpha eras (−1.3 days [95% CI −2.3, −0.4]). Interpretation: Our study suggested that MIS-C clinical phenotypes varied across SARS-CoV-2 eras, with patients in Delta and Omicron eras being younger and less sick. EHR data can be effectively leveraged to identify rare complications of pandemic diseases and their variation over time. Funding: None